- #1
ddr
- 8
- 0
Homework Statement
4
∫ √x/(1+√x)
0
Homework Equations
The Attempt at a Solution
t=√x ; x=t^2 ; dx= 2t
2
∫ (2t^2)/(1+t)
0
and now?
thanx
How Do You Solve the Integral of √x/(1+√x) from 0 to 4?
- Thread starter ddr
- Start date
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- Tags
- Integral
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SUMMARY
The integral of √x/(1+√x) from 0 to 4 can be solved using substitution and polynomial algebraic division. By letting t=√x, the integral transforms into 2∫ (2t^2)/(1+t) dt. To simplify the denominator, it is recommended to perform polynomial algebraic division on the resulting expression. This method allows for direct integration of the simplified result.
PREREQUISITES- Understanding of integral calculus
- Familiarity with substitution methods in integration
- Knowledge of polynomial algebraic division
- Basic skills in manipulating algebraic expressions
- Study techniques for performing substitutions in integrals
- Learn about polynomial algebraic division and its applications in calculus
- Explore advanced integration techniques such as integration by parts
- Practice solving definite integrals with variable substitutions
Students studying calculus, particularly those focusing on integration techniques, and educators looking for examples of integral simplification methods.